The Second Battalion of Light-Infantry led the Column, supported by the 2nd of Grenadiers, with the 33rd and 64th Regiments; these, commanded by Major-General Gray, marched from the New-Bridge at Nine oClock on Sunday Evening, and between One and Two in the Morning arrived at the Rebel Cantonments; Major Straubenzie had been detached with Six Companies of the same Battalion of Light-Infantry, the other Six under the Honourable Major Maitland, kept the Road, by which Manuvres the Enemys Patroll, consisting of a Serjeant and about a Dozen Men, was entirely cut off. Major Straubenzie moved on with the 71st Light-Company, and in a Small Village surprised a Party of Virginia Cavalry, stiled Mrs. Washingtons Guards, consisting of more than an Hundred, commanded by Lieut. Col. Baylor, who, with Major MLeod, and two other Officers, upon forcing the Door of an House, attempted to get up a large Dutch Chimney; the Two former were mortally wounded, the Third killed, and the Fourth made Prisoner; from hence a Part of Sir James Bairds Company was detached to a Barn where 16 Privates were lodged, who discharged 10 or 12 Pistols, and striking at the Troops sans Effet with their Broad Swords, Nine of them were instantly bayoneted and seven received quarter. Major Maitlands Force coming up at that Time attacked the Remainder of the Rebel Detachment, lodged in several other Barns, with such Alertness as prevented all but three Privates from making their Escape. The Troops lay on their Arms till Break of Day, when moving forward, the Light-Infantry fell in with a Volunteer Company of Militia in a very Thick Wood and Swamp, these gave one Fire, which the 40th Company, commanded by Capt. Montgomery, returned, and drove them off, leaving 6 Dead, but afterwards scampering across the Road, in Front of a Company of Grenadiers, three more were killed by them. The Light-Infantry, in pursuing them, up to Tapan, where they were intirely dispersed, took five Prisoners, all of them wounded. The whole Loss on this Occasion was one Private of 2nd Battalion Light-Infantry, killed. Upon entering the abovementioned House, one of the Rebel Officers demanded the Name of the Corps which had attacked them, was answered the British Light-Infantry, on which he exclaimed---Then we shall be all cut off.

General Washington, with his Army, we hear crossed the North-River, near Dobbs Ferry, into New-Jersey, last Saturday; and the Day before a large Body of Militia, and some continental Troops, marched from Woodbridge, Elizabeth-Town, &c. under the Command of the Generals Maxwell and Heard, for Hackinsack.

Among the Rebel Prisoners lately taken in New-Jersey, and brought here, is a Major Van Beuren, from Albany, who is well known by many respectable Refugees now here, for his Activity in apprehending and imprisoning the Loyalists: He was Master of the Ceremony at the Declaration of Independence in Albany; at the Close of that Day, he conducted with great Pomp, the burning of the Kings Arms, formerly deposited at an Ornament in the Court-Hall, and expressed monstrous Indignity on that Occasion, against the King and his Friends: In short, he has been instrumental to many Acts of Tyranny and Oppression to the Kings Friends; as a Reward for his meritorious Deeds---to encourage the Spirit of Rebellion, and to discourage that of Loyalty, and on the Principle to return Good for Evil, perhaps some pretended Friend to Government may intercede for his Release.

Col. Baylor and Major McLeod are both dead of the Wounds they received at Tappan on Sunday Night the 27th Instant, as mentioned in the Second Page of this Paper.

General Washington did not cross the North-River, with his Army, as mentioned in our last; we are told, he is in and about Peeks-Kill, Fish-Kill, and Danbury, with a pretty considerable Body of Men.

The New-York Gazette and the Weekly Mercury, October 12, 1778. NEW-YORK, September 26 [1778.]

Thursday last 29 rebel prisoners were brought to this city from New Jersey.

The Royal Gazette (New York,) September 26, 1778. NEW-YORK, September 30 [1778.]

The following account was brought to the Printer by an Officer present in the affairs and just arrived from English Neighbourhood, in New Jersey. Our commander having information that 200 rebel militia were cantoned in the neighbourhood of Hackinsack; a little after eleven on Sunday night, ordered the troops to march, but two privates deserting, gave notice of our approach; the enemy pushed off, and our intention was frustrated. However we were more successful in another object; the second battalion of light-infantry, with the seventy-first regiment, and the Queens Rangers, who had passed the Hudson at Dobbs ferry, were engaged in it. These fell in with the third Virginia battalion, distinguished by the appellation of Washingtons Guards, consisting of very well appointed cavalry with extreme good horses and neat accoutrements, our troops dashed upon them with their bayonets: to such effect, that only three of that corps escaped; sixty, including five officers, were killed, with a number, as yet unknown, of the militia. The prisoners consist of 50 Virginians, many of whom are wounded: Col. Baylor, their commander, who is mortally Wounded, and left on his parole, wrote to General Washington, That he was very much mortified in being obliged to acquaint him that his whole regiment was killed or taken by the British &c. All their horses, accoutrements, &c. was brought in, with 300 cattle, a great quantity of sheep, &c. &c. The action happened near Tapan, and there was not one man in the British army hurt.

The prisoners, say that the establishment of this corps of Mr. Washingtons guards was 180, of these there were about 140 present in the affair; that Mr. Washington had, by a detachment to Boston, considerably weakened his army, with which he had moved towards Poughkeepsie. Anecdote of Major MLeod. He was a native of Ireland, formerly an adjutant in the Norwich militia, then a non commissioned officer in the horse guards, afterwards, by letter from a person in the minority, recommended to employment in the rebel service, where he presently obtained the rank of Lieutenant and Adjutant under Lord Stirling, was stationed at Ticonderoga, and after a short time preferred to a Majority in Baylors cavalry, with whom he distinguished himself in forming that corps. Mr. Washingtons guards are said to have been the best appointed corps in his army.

The Royal Gazette (New York,) September 30, 1778. NEW-YORK, October 3 [1778.]

A more particular account of the affair near Tapan, in East Jersey, (mentioned in our last.)

The second battalion of light-infantry led the column, supported by the 2nd of grenadiers, with the 33rd and 64th regiments; these, commanded by Major General Gray, marched from New Bridge at nine oclock on Sunday evening, and between one and two in the morning arrived at the rebel cantonments; Major Straubenzie had been detached with six companies of the same battalion of light-infantry, the other six under the Honourable Major Maitland, kept the road, by which manuvres the enemys patroll, consisting of a serjeant and about a dozen men, was entirely cut off. Major Straubenzie moved on with the 71st light company, and in a small village surprised a party of Virginia cavalry, stiled Mrs. Washingtons Guards, consisting of more than an hundred, commanded by Lieut. Col. Baylor, who, with Major MLeod, and two other officers, upon forcing the door of an house, attempted to get up a large Dutch chimney; the two former were mortally wounded, the third killed, and the fourth made prisoner; from hence a part of Sir James Bairds company was detached to a barn where 16 privates were lodged, who discharged 10 or 12 pistols, and striking at the troops sans Effet with their broad swords, nine of them were instantly bayoneted and seven received quarter. Major Maitlands force coming up at that time attacked the remainder of the rebel detachment, lodged in several other barns, with such alertness as prevented all but three privates from making their escape. The troops lay on their arms till break of day, when moving forward, the light infantry Fell in with a volunteer company of militia in a very thick wood and swamp, these gave one fire, which the 40th company, commanded by Capt. Montgomery, returned, and drove them off, leaving 6 dead, but afterwards scampering across a road, in front of a company of our grenadiers, three more were killed by them. The light infantry, in pursuing them up to Tapan, where they were intirely dispersed, took five prisoners, all of them wounded. The whole loss on this occasion was one private of 2nd battalion light-infantry killed. Upon entering the abovementioned house, one of the rebel officers demanded the name of the corps, which had attacked them, was answered the British light-infantry, on which he exclaimed---Then we shall all be cut off.

The Royal Gazette (New York,) October 3, 1778. NEW-YORK, October 3 [1778.]

Several gentlemen lately Arrived from New-Bridge in East-Jersey, mention that Lieut. Col. Baylor, and Major MLeod, are both dead of their wounds, they received last Sunday night from the Coup de Main effected by the 2nd battalion of Light Infantry.

The Royal Gazette (New York,) October 3, 1778. NEW-YORK, October 7 [1778.]

The following orders, written by Lieut. Colonel George Baylor, of Mrs. Washingtons dragoons, were picked up last Sunday sennight, the morning that ladys corps was surprised by the British light-infantry.

SIR, YOU are hereby instructed to enlist your proportion of men, which is the number of thirteen, in any part of the state of Virginia, with all imaginable dispatch, and bring them to Fredericksburg as soon as you have effected it, provided you cannot get all of your men in three weeks time, you are to send such as you may have enlisted to Fredericksburg, under the direction of some careful soldier or your serjeant. You are to enlist no man who is older than 26, or younger than 18 years of age, and not to exceed ten stone, 140 weight; you are to take none but active well made thin thighed men; the privates are to receive Twenty Dollars bounty and a suit of cloaths on entering into the service, and take the oath before a magistrate, and are to receive 2 : 10s. a month; they are to be raised to serve during the war, unless sooner discharged. Each non-commissioned officer and private is to be furnished with a good horse, saddle, bridle and other accoutrements belonging to the horse service at the expence of the Continent, and you are to take no man that is above five feet ten inches high, and none under five feet seven inches; each man is to furnish himself with a blanket, which he will be paid for.